22.106 Neutron Interactions and Applications (Spring 2005)
Problem Set No. 7
Due: May 3, 2005
The purpose of this Problem Set is primarily to go through the derivations of a number of
key results encountered in the lectures on the theoretical basis underlying thermal neutron
scattering and the dynamic structure factor S (k , ω ) .
Problem 1
Derive the Born approximation in neutron scattering , Eq. (15.26) in the Lecture Notes,
starting with the integral equation approach to potential scattering.
Problem 2
Investigate the validity of the Born approximation for thermal neutron scattering to show
whether or not the approximation is valid.
Problem 3
Give a detailed discussion of what is the Fermi psuedopotential. Why is it useful in
thermal neutron scattering?
Problem 4
Show the double differential neutron scattering cross section can be expressed in terms of
the dynamic structure factor, S (k , ω ) . Discuss briefly why this quantity is useful in the
study of structure and dynamics of physical systems. Can S (k , ω ) be calculated using
Monte Carlo or Molecular Dynamics simulation?